jax.numpy.fft.rfftn#

jax.numpy.fft.rfftn(a,s=None,axes=None,norm=None)[source]#

Compute a multidimensional discrete Fourier transform of a real-valued array.

JAX implementation ofnumpy.fft.rfftn().

Parameters:

• a (ArrayLike) – real-valued input array.

• s (Shape |None) – optional sequence of integers. Controls the effective size of the inputalong each specified axis. If not specified, it will default to thedimension of input alongaxes.

• axes (Sequence[int]|None) – optional sequence of integers, default=None. Specifies the axes alongwhich the transform is computed. If not specified, the transform is computedalong the lastlen(s) axes. If neitheraxes nors is specified,the transform is computed along all the axes.

• norm (str |None) – string, default=”backward”. The normalization mode. “backward”, “ortho”and “forward” are supported.

Returns:

An array containing the multidimensional discrete Fourier transform ofahaving size specified ins along the axesaxes except along the axisaxes[-1]. The size of the output along the axisaxes[-1] iss[-1]//2+1.

Return type:

Array

See also

• jax.numpy.fft.rfft(): Computes a one-dimensional discrete Fouriertransform of real-valued array.

• jax.numpy.fft.rfft2(): Computes a two-dimensional discrete Fouriertransform of real-valued array.

• jax.numpy.fft.irfftn(): Computes a real-valued multidimensional inversediscrete Fourier transform.

Examples

>>>x=jnp.array([[[1,3,5],...[2,4,6]],...[[7,9,11],...[8,10,12]]])>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfftn(x)Array([[[ 78.+0.j  , -12.+6.93j],        [ -6.+0.j  ,   0.+0.j  ]],       [[-36.+0.j  ,   0.+0.j  ],        [  0.+0.j  ,   0.+0.j  ]]], dtype=complex64)

Whens=[3,3,4], size of the transform alongaxes(-3,-2) willbe (3, 3), and alongaxis-1 will be4//2+1=3 and size alongother axes will be the same as that of input.

>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfftn(x,s=[3,3,4])Array([[[ 78.   +0.j  , -16.  -26.j  ,  26.   +0.j  ],        [ 15.  -36.37j, -16.12 +1.93j,   5.  -12.12j],        [ 15.  +36.37j,   8.12-11.93j,   5.  +12.12j]],       [[ -7.5 -49.36j, -20.45 +9.43j,  -2.5 -16.45j],        [-25.5  -7.79j,  -0.6 +11.96j,  -8.5  -2.6j ],        [ 19.5 -12.99j,  -8.33 -6.5j ,   6.5  -4.33j]],       [[ -7.5 +49.36j,  12.45 -4.43j,  -2.5 +16.45j],        [ 19.5 +12.99j,   0.33 -6.5j ,   6.5  +4.33j],        [-25.5  +7.79j,   4.6  +5.04j,  -8.5  +2.6j ]]], dtype=complex64)

Whens=[3,5] andaxes=(0,1), size of the transform alongaxis0will be3, alongaxis1 will be5//2+1=3 and dimension alongother axes will be same as that of input.

>>>withjnp.printoptions(precision=2,suppress=True):...jnp.fft.rfftn(x,s=[3,5],axes=[0,1])Array([[[ 18.   +0.j  ,  26.   +0.j  ,  34.   +0.j  ],        [ 11.09 -9.51j,  16.33-13.31j,  21.56-17.12j],        [ -0.09 -5.88j,   0.67 -8.23j,   1.44-10.58j]],       [[ -4.5 -12.99j,  -2.5 -16.45j,  -0.5 -19.92j],        [ -9.71 -6.3j , -10.05 -9.52j, -10.38-12.74j],        [ -4.95 +0.72j,  -5.78 -0.2j ,  -6.61 -1.12j]],       [[ -4.5 +12.99j,  -2.5 +16.45j,  -0.5 +19.92j],        [  3.47+10.11j,   6.43+11.42j,   9.38+12.74j],        [  3.19 +1.63j,   4.4  +1.38j,   5.61 +1.12j]]], dtype=complex64)

For 1-D input:

>>>x1=jnp.array([1,2,3,4])>>>jnp.fft.rfftn(x1)Array([10.+0.j, -2.+2.j, -2.+0.j], dtype=complex64)